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How can you plot the graph for the function $(\sin x)^x$? My problem is that $\sin(x)$ can assume negative values too, so it is not like a standard exponential function. Any help would be appreciated.

L.K.
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user34304
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  • I think it's not that easy to think of it. This work should be left over the computers. However I am having a graph which can explain this graph. http://i.imgur.com/4CpZPAg.png – Saharsh Jun 15 '14 at 06:53

3 Answers3

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Yep, the function (from $\mathbb{R}$ to $\mathbb{R}$) is not defined for all real numbers, so we need to make a restriction on the domain from all the reals to the sets $\ldots(-4\pi,-3\pi)$, $(-2\pi,-\pi)$, $(0, \pi)$, $(2\pi, 3\pi)$, $(4\pi, 5\pi)\ldots$ in order to have a well defined function. Hopefully this helps.

Plot of the graph

mattapow
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  • When thinking of composite functions like this I find it helps to graph the first one (i.e. sin(x)) and then think of taking the second function in the composition (i.e. ^x). – mattapow Jun 15 '14 at 07:16
  • Although, it is actually a well defined function from the reals into the complex numbers. – mattapow Jun 15 '14 at 07:33
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I think we can change the undefined points to be defined, for example, we can plot the graph for the function $|\sin x|^x$ first. Then because those values of $x$ which make $\sin x<0$ are not in the domain, we can erase them from the graph. enter image description here

Ng Chikeung
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It's quite difficult to plot these points and making the guesses about it, however I am not saying it's impossible but it'll take you forever. So here I am providing you it's graph to make it easier.

$$(\sin x)^x$$

enter image description here

Saharsh
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